### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2pPA6. Reflections on the nonlinear equation of state in rock based on
experiment.

**James A. TenCate
**

**
**
*EES-4 MS D443, Los Alamos Natl. Lab., Los Alamos, NM 87545
*

*
*
Measurements were made of the propagation of 1-D nonlinear waves (i.e.,
Young's mode) in a bar of Berea sandstone 3.8 cm in diameter and 1.8 m long.
Both waveforms (time domain) and spectra (frequency domain) were measured. The
experimental results were then compared with waveforms calculated from a
numerical scheme based on the simple wave solution for 1-D waves in rock using a
classical nonlinear equation of state. The numerical solution is written in
MATLAB and runs quickly on a small personal computer. Attenuation was added by
propagating the waveform a small distance, transforming the waveform into the
frequency domain, and applying the attenuation, and then transforming back into
the time domain and propagating the new waveform. The same method was applied
earlier for nonlinear propagation of a sound wave in a tube of air by Pestorius
and Blackstock. The experiments and simulations clearly demonstrate that a
classical nonlinear equation of state is incomplete or inappropriate for
describing or modeling nonlinear propagation in sandstone. Results from another
model (Van Den Abeele, this session) suggest the same conclusions. [Work
supported by OBES/DOE through the University of California.]